NP is as easy as detecting unique solutions
Theoretical Computer Science
Trading group theory for randomness
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Journal of the ACM (JACM)
Algebraic methods for interactive proof systems
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Parallelization, amplification, and exponential time simulation of quantum interactive proof systems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Classical and Quantum Computation
Classical and Quantum Computation
Robust pcps of proximity, shorter pcps and applications to coding
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Consequences and Limits of Nonlocal Strategies
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Assignment Testers: Towards a Combinatorial Proof of the PCP-Theorem
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
The Complexity of the Local Hamiltonian Problem
SIAM Journal on Computing
The PCP theorem by gap amplification
Journal of the ACM (JACM)
Computational Complexity
The detectability lemma and quantum gap amplification
Proceedings of the forty-first annual ACM symposium on Theory of computing
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
The Quantum and Classical Complexity of Translationally Invariant Tiling and Hamiltonian Problems
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Proceedings of the forty-second ACM symposium on Theory of computing
Commutative version of the local Hamiltonian problem and common eigenspace problem
Quantum Information & Computation
Approximation Algorithms for QMA-Complete Problems
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
The complexity of quantum spin systems on a two-dimensional square lattice
Quantum Information & Computation
On perfect completeness for QMA
Quantum Information & Computation
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Approximating CSPs with global cardinality constraints using SDP hierarchies
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Consistency of local density matrices is QMA-Complete
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Complexity of commuting Hamiltonians on a square lattice of qubits
Quantum Information & Computation
A note about a partial no-go theorem for quantum PCP
Quantum Information & Computation
A Multi-prover Interactive Proof for NEXP Sound against Entangled Provers
FOCS '12 Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
A classical leash for a quantum system: command of quantum systems via rigidity of CHSH games
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Trivial low energy states for commuting Hamiltonians, and the quantum PCP conjecture
Quantum Information & Computation
Product-state approximations to quantum ground states
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Hi-index | 0.00 |
The classical PCP theorem is arguably the most important achievement of classical complexity theory in the past quarter century. In recent years, researchers in quantum computational complexity have tried to identify approaches and develop tools that address the question: does a quantum version of the PCP theorem hold? The story of this study starts with classical complexity and takes unexpected turns providing fascinating vistas on the foundations of quantum mechanics and multipartite entanglement, topology and the so-called phenomenon of topological order, quantum error correction, information theory, and much more; it raises questions that touch upon some of the most fundamental issues at the heart of our understanding of quantum mechanics. At this point, the jury is still out as to whether or not such a theorem holds. This survey aims to provide a snapshot of the status in this ongoing story, tailored to a general theory-of-CS audience.